Distortion correction system



March 8, 1966 s, KENDALL 3,238,909

DISTORTION CORRECTION SYSTEM Filed June 15, 1964 4 Sheets-Sheet 1 INVENTOR.

SAM KENDALL BY ,e am m r MW 5 ATTORNEYS March 8, 1966 s. KENDALL 3,238,909

DISTORTION CORRECTION SYSTEM Filed June 15, 1964 4 Sheets-Sheet 2 as T INVENTOR SAM KENDALL BYMWIM MaZZKLQ/S m; ATTORNEYS March 8, 1966 s. KENDALL 3,238,909

DISTORTION CORRECTION SYSTEM Filed June 15, 1964 4 Sheets-Sheet 8 INVENTOR SAM KENDALL ff/J ATTORNEYS March 8, 1966 5, KENDALL 3,238,909

DISTORTION CORRECTION SYSTEM Filed June 15, 1964 4 Sheets-Sheet 4 INVENTOR SAM KENDALL BY Ag. ,2 Mum #15 ATTORNEYS United States Patent ()fiice 3,238,909 Patented Mar. 8, 1966 3,238,909 DISTORTION CORRECTION SYSTEM Sam Kendall, Richmond, Va., assignor to Reynolds Metals Company, Richmond, Va., a corporation of Delaware Filed June 15,1964, Ser. No. 374,946 15 Claims. (Cl. 113-120) This application is a continuation-in-part of my copending application Serial No. 197,679, filed May 25, 1962, now abandoned and entitled, Distortion Correction System, and the invention relates to a system of compensatory optical distortion for preparing from undistorted copy a copy having a predetermined distortion to offset a subsequent opposite distortion, especially for preparing preprinted flat stock for production of drawn containers and the like.

It has been known that flat metal stock can be preprinted and drawn into a desired article, such as a cylindrical container, and that the preprinting on the flat stock can be distorted in such a manner as to compensate for the distortion caused by the drawing operation, with the result that the preprinted art work on the flat stock will appear on the finished article in approximately its intended form. However, this has evidently been done on a trial and error basis, which is extremely diflicult and time consuming in the case of a relatively complicated design, especially where fine print is involved, such as the list of ingredients required on food cans, or where a halftone or line picture is shown.

The present invention provides an optical system of determining the necessary distortion from an original undistorted design copy for preprinting distorted copy on flat stock so that a subsequent drawing operation will restore the original copy. As a result, it is possible to preprint complicated designs, including fine print and pictures, in such a way as to greatly reduce the time necessary to determine how to print the necessary distorted design on the flat stock, and to do so with greater precision. The present invention includes preprinting on flat stock a continuous printed coating which will extend entirely across the closed end and up the adjacent sides of a drawn container, thus producing an attractive and economical new form of decorated container, especially when printed on the sides and across the closed end with the lid on the other end serving as the bottom. Alternatively, in accordance with certain embodiments, the invention includes preprinting on fiat stock a coating which extends solely over areas of the stock which are to be on sides of a drawn product.

For better understanding of the invention reference is now made to the accompanying drawings, in which there is shown, for purposes of illustration only, present preferred embodiments of the invention. In the drawings:

FIG. 1 shows the original art work which is intended to appear on the sides of a cylindrical metal container;

FIG. 2 shows the art work of FIG. 1 being photographed through a lens which distorts in one direction;

FIG. 3 shows the photograph made as illustrated in FIG. 2, with the horizontal dimensions unchanged but the vertical dimensions proportionally increased;

FIG. 4 shows the copy illustrated in FIG. 3 mounted in a special reflector and the reflected image being photographed by a camera;

FIG. 5 shows the picture taken by the camera in FIG. 4 as printed on flat metal stock;

FIG. 6 shows diagrammatic drawing apparatus and the metal stock of FIG. 5 after it has been drawn into a cylindrical container;

FIGS. 7, 8 and 9 show side elevational views of the cylindrical container after it has been formed as shown in FIG. 6, in which FIG. 7 shows one side view, FIG. 8

shows the side on the right of FIG. 7, and FIG. 9 the opposite side from that shown in FIG. '7;

FIG. 10 shows a modification of FIG. 5, in which a central design is added to cover the closed end of the container;

FIG. 11 shows a view of the closed end of the container made from the pre-printed stock shown in FIG. 10; and

FIG. 12 shows a perspective view of the container shown in FIG. 11, with part of the decoration omitted and a lid added to close the bottom of the container.

Referring now more particularly to the drawings, FIG. 1 shows an example of art work as originally laid out and intended to be reproduced on the sides of the container shown in FIGS. 7-9. The art work 10 is divided into four general panel areas 11, 12, 14 and 16 of the same size and separated by diagonal lines 18, 19, 20 and 21. The panel 12 has an oval 23 in the middle and four triangles 22 arranged in the positions of the corners of a rectangle around the oval 23. The panel 14 has a square 24 in its center, and the panel 16 has a series of parallel lines 26. For purposes of simplicity, no actual printing is shown in FIG. 1, but blocks of print can readily be imagined in the square 24 and along the lines 26, and the oval 23 could, for example, be in the form of a trademark of any design, with or without printing. The various portions of the art work 10 are substantially uniformly proportional in size to a reproduction thereof which is to occur on the side surface of the drawn product. The upper horizontal edge of the art work 10 is designated A and the lower horizontal edge is designated B, while the two side edges are designated C. The length of the edges A and B are shown to be equal to the circumference of the final outside cylindrical surface of the container, and the length of the sides C is shown to be equal to the height of the container, or that portion of the height of the container which is to be printed.

In order to accomplish distortion of the art work 10, it is first mounted on a copy board and photographed through an oil-filled prism 42 by a camera 44. The prism 42 has a flat surface 41 parallel to and facing the copy 10, and a cylindrical surface 43 on the other side which has the effect of increasing the lengths of the sides C of the art work relative to the length of the sides A and B. The resultant copy work 10 is shown in FIG. 3, where the sides A and B are shown as having the same length, while the sides C are longer than the sides C shown in FIG. 1. The figures and designs in the art work are correspondingly elongated vertically as shown in FIG. 3 relative to their vertical dimensions in FIG. 1, while their horizontal dimensions remain unchanged. Thus, the several portions of the art Work, though elongated vertically, still are substantially uniformly proportional in size to a reproduction thereof which is to :occur on the side surface of the drawn product.

The art work 10' shown in FIG. 3 can he in the form of a photographic negative film, which is wrapped around the outside of a transparent cylindrical glass support shown in FIG. 4. The cylinder 60 is mounted coaxially with a mirror 62 which preferably is substantially in the form of a truncated cone, or otherwise nevertheless has a viewing surface which is characterized by having curva ture which progressively sharpens around the centralaxis of the mirror with progressively decreasing distance between the art work 10 and the viewing surface of the mirror for the image of the art work as viewed in the mirror in the direction of the central axis of the mirror to have distortion which is to compensate for distortion of the stock when the stock is being drawn from flat form to the contour of the drawn product. As shown, the truncated conical mirror 62 has its viewing surface inclined at an angle of about 45 degrees with respect to the central axis of the mirror. A light bulb 64 is-mounted concentrically within the cylinder 60, and casts light through the cylinder 60, the negative film containing the art work 10, and the resultant reflection of the art work 10' on the mirror 62 is photographed by a camera 66 mounted with the central axis of its lens in line with the central axes of cylinder 60, mirror 62 and light bulb 64. An opaque cap 65 is mounted in the cylinder 60 to shield the camera lens from the direct light of the bulb 64.

When the negative containing the art work 10' is wrapped around the supporting cylinder 60 the opposite edges C of the negative just meet, and consequently the image of the art work 10' reflected from mirror 62 is photographed by the camera 66 in the form of a circle, which is preprinted on the fiat metal stock 76 as shown in FIG. 6. For economy, multiple duplicates of the design are printed on the stock while it is in coil or sheet form. The stock 70 is preferably aluminum, especially rolled aluminum can stock, but may be copper, steel, tin or other ductile metals or metal alloys, in solid, plated or other forms, or may be of other ductile sheet materials, such as polymeric plastics.

The circular art work 10 shown in FIG. has an outer circular edge A", and an inner circular edge B corresponding respectively to the edges A and B of the art work shown in FIG. 1. In order to obtain this orientation, the edge A shown in FIG. 3 is placed nearest to the camera as shown in FIG. 4, while the opposite edge B is placed farthest from the camera as shown in FIG. 4. When the base lines B and B and the circumference of B" are of equal length, as illustrated, the radial distance C" between the edges A and B" is substantially less than the length of the edge C shown in FIG. 1, but increases during the subsequent drawing operation to equal the length of the edge C shown in FIG. 1 (which is equal to the length C" of the decorated side of the container shown in FIGS. 79).

For purposes of illustration, the art work shown in FIGS. 1-9 is drawn accurately to the same scale. In practice, however, the scale of the art work in its various stages prior to the final printed design shown in FIG. 5 can be varied for convenience of the artist and photographer, and is preferably enlarged until the last stages of preparing prints of the design shown in Fig, 5. Usually the photographic film made in the camera in FIG. 4 is black-and-white, and it or a print made from it is given any retouching that may be desired. A master negative is then prepared, and a temporary opaque coating is applied to certain areas to determine the areas of a given color, in accordance with known practice. A film in final scale is made from the opaqued negative for purposes of printing that color in the design shown in FIG. 5, and a printing plate or the like is made from the film. The opaque coating is washed off and the process repeated for other colors, unless the final design is to be limited to a black-and-white or like two-color combination, in which case the stock 70 is uniformly coated with a background color, and only one printing plate or the like is used to print on it. A tough, adherent, elastic ink coating is used to print the design on the metal stock shown in FIG. 5, so that the coating will adhere and flex as the metal is deformed in the drawing operation shown in FIG. 5. Such inks are commercially available for the various printing processes, such as silk screen, Flexographic, dry offset, wet offset and rotogravure, and preferably are based on thermoplastic resins, such as vinyl chloride-vinyl acetate copolymers. Modified polyesters with an added catalyst are preferred as the ink resin if the container is to be packed with a product, such as certain foods, that must be processed at high temperatures after packing.

In a typical example of the operation shown in FIG. 4, the maximum inner diameter of the frusto-conical mirror 62 is about 19 inches, the distance from the mirror to the lens (14 inches focal length) is about inches, the film in the mirror has a circumferential length of slightly under 26 inches, and the outer diameter of the edge A" on the film made in camera 66 is about 10 inches. These dimensions can obviously be varied, but illustrate that the camera 66 need not be at a great distance from mirror 62.

FIG. 6 illustrates means for drawing the stock into a container such as a can body having one integrallyformed closed end. The stock 70, after being cut into a circle just beyond A", is slidably held between a die member and a ring 76, and a plunger 78 moves down to the position shown in FIG. 6 to draw the stock 70 into the can body shown in FIGS. 7-9. At the beginning of the drawing operation shown in FIG, 6 the preprinted art work 10 shown in FIG. 5 extends around the outside of the die cavity '7, with the inner circumference B" substantially coincident with the outer circumference of the die cavity 77 (or a little less if the side wall decoration is to extend over the rounded corner at the closed end of the container). As the plunger 78 moves down the radial distance C" shown in FIG. 5 is increased relatively slightly while successive circumferences outwardly of the circumference B are progressively contracted until finally the outer circumference A is reduced to equal the diameter of the circumference B, which is substantially unchanged during the drawing operation. If the side wall decoration extends over the rounded corner at the closed end of the container, the diameter B will remain a little less than the diameter of A".

When the distortions of the art work 10 shown in FIG. 5 are completed during the drawing operation shown in FIG. 6, the art work is restored to the form shown in FIG. 1, as will be apparent from inspection of FIGS. 7-9. It may be observed that the four panels 11, 12, 14 and 16 shown in FIG. 1 appear approximately on four quadrants of the finished can 80 shown in FIGS. 7-9, and that the diagonal lines 18, 19, 20 and 21 were used to separate these quadrants because some relatively simple design should be used for that purpose, since it is an observed fact that the maximum distortion of the art work on the final cylindrical body from that shown in the original layout occurs at four places around the circumference of the cylindrical can body spaced apart from each other. This is believed to be an effect caused by the orientation of the grain pattern in the rolled metal sheet from which the can stock 70 is preferably made. As shown in FIG. 5, the grain would run parallel to the upper and lower edges of sheet 70 if the sheet extends continuously left and right as shown in FIG. 5 when the design is printed on the sheet.

The amount of linear distortion which is to be accomplished by means of the prism 42 shown in FIG. 2 is determined experimentally. First, the amount of difference between the dimension C of the preprinted circular design shown in FIG. 5 as compared to the height C" of the can body shown in FIGS. 79 is determined experimentally. Also determined experimentally is the distortion of dimension C resulting from perspective effects when the camera 66 photographs the mirror 62 shown in FIG. 4. It is not practical to locate the camera 66 an infinite distance from the mirror 62, and consequently some perspective distortion will result. This distortion tends to reduce the dimension C" shown in FIG. 5. Consequently, prism 42 or the like is used to increase the dimension shown at C in FIG. 1 sufiiciently to offset the reduction of this dimension in the operation shown in FIG. 4 just enough so that the increase of that dimension by the operation shown in FIG. 6 will make the final height C equal the original dimension C.

The invention can also be applied to a continuous side and end coating of a closed-end drawn container, which is particularly attractive if the printing on the side is oriented so that the printed closed-end becomes the top of the container, with a conventional cap across the bottom of the container serving as the base. In order to accomplish this result, the design shown in FIG. 5 is modified as shown in FIG. 10 to add decorative .printing in the area surrounded by the edge B" in FIG. 5 (e.g., stripes 71 and 72 respectively joining stripes 18 and 20, and 19 and 21). The background color of the central decoration preferably merges with the background color on the outside of edge B, so that this edge disappears. FIG. 11 shows the decorated closed end of a container 80 drawn from the decorated flat stock 7 shown in FIG. 10, and FIG. 11 shows a perspective view of the container 80', with side and top shown on its side and closed end to illustrate printing oriented to make the closed end the top of the container (portions of the decoration shown in the other figures are omitted for convenience of illustration). The closed end is not distorted during the drawing operation, and very little by the shallow circular channels or the like which are conventionally impressed in the closed ends of drawn containers. The closed end, therefore, is a good place for fine print, as this is the print most affected by any slight distortions which may occur when the printed side Wall is drawn.

In other embodiments still in accordance with the pre ent invention, the art work 10, mounted flat on copy board 40, as in FIG. 2, is-copied by use of camera 44 while the distorting prism 42 is omitted from the step represented by FIG. 2, and the art Work in the resulting substantially true undistorted fiat photograph is characterized by having substantially the same vertical dimension to horizontal dimension ratio as do comparable vertical and horizontal dimensions of the art work which is to occur in reproduced form on the drawn product, and conveniently the photograph taken by the camera 44 is a photographic negative which, instead of the distorted copy 10' indicated in FIG. 3, is wrapped around the cylindrical glass support 60 and is associated with a particular mirror 62 that in and of itself gives a properly distorted image of the art work from the undistorted copy of the work on the cylindrical glass support 60. Photographing the latter distorted image by use of camera 66 as in FIG. 4 thereafter ensues, this stock is preprinted from the latter image .as in accordance with the general procedures indicated hereinbefore, and the preprinted stock is drawn and thereby forms a resulting drawn product including a substantially true reproduction of the art work 10.

A distorted image is achieved by one of various mirrors 62, these preferably being of frusto-conical type and each having a different angle of inclination of its viewing surface with respect to the corresponding central axis of the mirror. Any one of the mirrors, as need be, is used by being disposed concentrically coaxially with the cylindrical glass support 60. The magnitude of distortion in the mirror image of the art work in accordance with the latter practices increases with increase in the angle of inclination of the viewing surface of the mirror with respect to the mirror axis from mirror to mirror in a direction corresponding to that of the dimension C in FIG. 5. The omission of a prism 42 therefore is tolerated in those instances where the inclination of the viewing surface of the particular mirror 62, with respect to the central axis of the mirror, renders the mirror in and of itself sufficient to produce the desired distorted mirror image of the art work to the camera 66 and thus a proper dimension C" (FIG. to compensate for a particular drawing operation to which the preprinted flat stock is to be subjected.

Thus, in certain instances the particular mirror 62 used in the system serves adequately to achieve desired distortion, and accordingly the desired value of the dimension C" needed to attain the dimension C and a substantially true reproduction of the art work on the drawn product, although the art work as imaged by the mirror in the system has not been appreciably pre-distorted except by the mirror itself. However, it remains that in the practice of the present invention, the use of any of a variety of prisms 42, or the like, in the step represented in FIG. 2, is nevertheless often preferred. For example, it is usually easier and less expensive to provide a particular prism 42 from a selection of such prisms in order to make a particular mirror 62 work satisfactorily for immediate demands, than it is to alter the mirror or replace it to meet varying needs.

It will be apparent to those skilled in the art that the invention is applicable to preprinted ductile flat stock drawn into shapes other than cylinders; for example, the invention is applicable to making containers drawn into conical shapes or into other shapes which have cylindrically or conically shaped portions in their side walls (e.g., straight side walls with cylindrically or conically curved corners). Also, the invention is applicable to interior as well as to exterior decorations.

While present preferred embodiments of the invention and present preferred methods of practicing the same have been illustrated and described, it will be understood that the invention is not limited thereto, but only by the scope of the following claims.

I claim:

1. In a method of making preprinted flat stock which is to be drawn into curved product form, the art which includes providing a design having portions substantially uniformly proportional to corresponding portions of a curved substantially true reproduction of the design which is to occur on the curved surface of the drawn product, optically impinging said proportional design upon a viewing surface characterized by having a shape such that the distance between its longitudinal axis and intersections of said surface with planes containing said axis decreases from one end of said surface to the other and a curvature which progressively increases around said axis with progressively decreasing distance between said proportional design as the object and said viewing surface, for an image of said design on said viewing surface as viewed in the direction of said axis to have distortion which is to be compensated by distortion of the stock when the stock is being drawn from flat form to the curvature of the product, and printing in proper size onto portions of the stock, which are to be formed curved by drawing, a copy of said image corresponding to a view thereof along said axis, for a curved substantially true reproduction of said design to be produced on the curved product when the fiat stock is drawn.

2. In the method of claim 1, making a photographic copy of said image on the viewing surface viewed in the direction of said axis, and said image printed in copy on the fiat stock being derived from said photographic copy.

3. In the method of claim 1, making a photographic copy of said image on the viewing surface viewed in the direction of said axis, and producing color separation negatives from said photographic copy, said image printed in copy on the fiat stock being a color copy made from said color separation negatives.

4. In the method of claim 1, said copy of said image being printed on portions of the flat stock which are to be drawn to form an annular wall, and drawing the printed fiat stock into a product having in form the annular wall and a closed end.

5. In the method of claim 4, printing the surface of the fiat stock which is to be drawn to form the exterior surface of the annular wall.

6. In the method of claim 4, printing portions of the fiat stock prior to drawing which are to be in the closed end.

7. In the method of claim 4, printing the surfaces of the fiat stock prior to drawing which are to be external on the annular Wall and external on the closed end and orienting the printing to make the external surface of the closed end the top of the product.

8. In a method of making preprinted fiat stock which is to be drawn into curved product form, the art which includes providing a design having portions substantially uniformly proportional to corresponding portions of a curved substantially t-rue reproduction of the design which is to occur on the curved surface of the drawn product, optically impinging said proportional design upon a substantially conical viewing surface for an image of said design on said viewing surface as viewed axially of said viewing surface to have distortion which is to be compensated by distortion of the stock when the stock is being drawn from flat form to the curvature of the product, and printing in proper size onto portions of the stock, which are to be formed curved by drawing, a copy of said image corresponding to a view thereof along said axis, for a curved substantially true reproduction of said design to be produced on the curved product when the flat stock is drawn.

9. In a method of making preprinted flat stock which is to be drawn into curved product form, the art which includes providing a design having substantially the same vertical dimension to horizontal dimension ratio as comparable vertical and horizontal dimensions of a curved substantially true reproduction of the design which is to occur on the curved surface of the drawn product, optically impinging said design having said dimension ratio upon a viewing surface characterized by having a shape such that the distance between its longitudinal axis and intersections of said surface with planes containing said axis decreases from one end of said surface to the other and a curvature which progressively increases around said axis with progressively decreasing distance between said design having said ratio as object and said viewing surface, for an image of said design on said viewing surface as viewed in the direction of said axis to have distortion which is to be compensated by distortion of the stock when the stock is being drawn from flat form to the curvature of the product, and printing in proper size onto portions of the stock, which are to be formed curved by drawing, a copy of said image corresponding to a view thereof along said axis, for a curved substantially true reproduction of said design to be produced on the curved product when the fiat stock is drawn.

10. In a method of making preprinted flat stock which is to be drawn into curved product form, the art which includes providing a design having substantially the same vertical dimension to horizontal dimension ratio as comparable vertical and horizontal dimensions of a curved substantially true reproduction of the design which is to occur on the curved surface of the drawn product, optically impinging said design having said dimension ratio upon a substantially conical viewing surface for an image of said design on said viewing surface as viewed axially of said viewing surface to have distortion which is to be compensated by distortion of the stock when the stock is being drawn from flat form to the curvature of the product, and printing in proper size onto portions of the stock, which are to be formed curved by drawing, a copy of said image corresponding to a view thereof along said axis, for a curved substantially true reproduction of said design to be produced on the curved product when the fiat stock is drawn.

11. In a method of making preprinted fiat stock which is to be drawn into curved product form, the art which includes providing from a flat design a copy thereof having portions substantially uniformly proportional to corresponding portions of a curved substantially true reproduction of the design which is to occur on the curved surface of the drawn product, conforming said copy to a cylindrical support and optically impinging said copy upon a substantially conical viewing surface disposed co-axially with said support for an image of said copy on said viewing surface as viewed in the direction of the axes of said support and viewing surface to have distortion which is to be compensated by distortion of the stock when the stock is being drawn from flat form to the curvature ofthe product, and printing in proper size onto portions of the stock, which are to be formed curved by drawing, a copy of said image corresponding to a view thereof along said axis, for a curved substantially true reproduction of said designed to be produced on the curved product when the fiat stock is drawn.

12. In the method of claim 11, making photographical- 1y said copy from said fiat design and conforming the photographic copy to the cylindrical support, and making a photographic copy of said image on said viewing surface viewed in the direction of said axis, and said image printed in copy on the flat stock being derived from said photographic copy of the image on the viewing surface.

13. In a method of making preprinted flat stock which is to be drawn into curved product form, the art which includes providing from a flat design a copy thereof having substantially the same vertical dimension to horizontal dimension ratio as comparable vertical and horizontal dimensions of a curved substantially true reproduction of the design which is to occur on the curved surface of the drawn product, conforming said copy to a cylindrical support and optically impinging said copy upon a substantially conical viewing surface disposed co-axially with said support for an image of said copy on said viewing surface as viewed in the direction of the axes of said support and viewing surface to have distortion which is to be compensated by distortion of the stock when the stock is being drawn from flat form to the curvature of the product, and printing in proper size onto portions of the stock, which are to be formed curved by drawing, a copy of said image corresponding to a view thereof along said axis, for a curved substantially true reproduction of said design to be produced on the curved product when the fiat stock is drawn.

14. In the method of preprinting fiat stock and drawing it into conical form, the steps of making an undistorted copy of the design to be shown around the sides of the drawn article, said design having a form corresponding to that of a label adapted to be wrapped around the article to produce the desired design on the article, making a distorted copy of said design through a lens which increases the dimensions in one direction relative to those in a direction at right angles thereto, said direction being generally in the direction in which the drawing operation is to be performed, placing said first distorted copy in a conical mirror and making a second distorted copy of the image viewed in the conical mirror, and printing a copy of said distorted copy on the flat stock to be drawn into the finished article.

15. A method of preprinting flat stock and drawing it into a cupped product having circular cross sections, comprising the steps of making a copy of the design to be shown around the sides of the drawn product, arranging said copy of said design in the form of a cylinder and positioning it concentrically within a conical mirror, copying the reflection of said copy from the conical mirror, the copy made from said reflection being in the form of a circular band, and the ratio of the difference between the inner and outer radii of said band relative to the inner circumference of the said band being less than the ratio of the height of the original copy relative to its width, printing a copy of said circular band on flat stock, and drawing the printed flat stock to produce a cupped product having substantially the original design printed around its periphery.

References Cited by the Examiner UNITED STATES PATENTS 2,202,464 5/1940 Pattison 10l--426 2,617,337 11/1952 Snyder 9646 2,684,104 7/1954 Dessort 41255 3,073,210 1/1963 Packard 8824 3,122,437 2/1964 Collins 35-40 XR CHARLES W. LANHAM, Primary Examiner. 

1. IN A METHOD OF MAKING PREPRINTED FLAT STOCK WHICH IS TO BE DRAWN INTO CURVED PRODUCT FORM, THE ART WHICH INCLUDES PROVIDING A DESIGN HAVING PORTIONS SUBSTANTIALLY UNIFORMLY PROPORTIONAL TO CORRESPONDING PORTIONS OF A CURVED SUBSTANTIALLY TRUE REPRODUCTION OF THE DESIGNED WHICH IS TO OCCUR ON THE CURVED SURFACE OF THE DRAWN PRODUCT, OPTICALLY IMPINGING SAID PROPORTIONAL DESIGN UPON A VIEWING SURFACE CHARACTERIZED BY HAVING A SHAPE SUCH THAT THE DISTANCE BETWEEN ITS LONGITUDINAL AXIS AND INTERSECTIONS OF SAID SURFACE WITH PLANES CONTAINING SAID AXIS DECREASES FROM ONE END OF SAID SURFACES TO THE OTHER AND A CURVATURE WHICH PROGRESSIVELY INCREASES AROUND SAID AXIS WITH PROGRESSIVELY DECREASING DISTANCE BETWEEN SAID PROPORTIONAL DESIGN AS THE OBJECT AND SAID VIEWING SURFACE, FOR AN IMAGE OF SAID DESIGN ON SAID VIEWING SURFACE AS VIEWED IN THE DIRECTION OF SAID AXIS TO HAVE DISTORTION WHICH IS TO BE COMPENSATED BY DISTORTION OF THE STOCK WHEN THE STOCK IS BEING DRAWN FROM FLAT FORM TO THE CURVATURE OF THE PRODUCT, AND PRINTING IN PROPER SIZE ONTO PORTIONS OF THE STOCK, WHICH ARE TO BE FORMED CURVED BY DRAWING, A COPY OF SAID IMAGE CORRESPONDING TO A VIEW THEREOF ALONG SAID AXIS, FOR A CURVED SUBSTANTIALLY TRUE REPRODUCTION OF SAID DESIGN TO BE PRODUCED ON THE CURVED PRODUCT WHEN THE FLAT STOCK IS DRAWN. 